Long ranged singlet proximity effect in ferromagnetic nanowires

TL;DR

This paper demonstrates that in one-dimensional ballistic ferromagnetic nanowires, the standard singlet superconductor/ferromagnet proximity effect can be long ranged, with decay length linked to the electronic mean-free path, challenging previous assumptions.

Contribution

The study provides an exact solution showing the long ranged singlet proximity effect in ballistic 1D ferromagnetic nanowires, clarifying the nature of the effect without magnetic domains.

Findings

Proximity effect becomes long ranged in 1D ballistic regime.

Decay length equals the electronic mean-free path in a specific regime.

Discussion of experiments to determine the nature of the effect.

Abstract

Recently a long ranged superconductor/ferromagnet (S/F) proximity effect has been reported in Co crystalline nanowires [1, Nature, 6 389 (2010)]. Since the authors of [1] take care to avoid the existence of magnetic domains, the triplet character of the long ranged proximity effect is improbable. Here we demonstrate that in the one-dimensional ballistic regime the standard singlet S/F proximity effect becomes long ranged. We provide an exact solution for the decay of the superconducting correlations near critical temperature ($T_{c}$) and for arbitrary impurities concentration. In particular we find a specific regime, between the diffusive and ballistic ones, where the decay length is simply the electronic mean-free path. Finally possible experiments which could permit to elucidate the nature of the observed long ranged proximity effect in Co nanowires are discussed.